How do i learn limits? What are they for? This really look like useless rocket science now, my teacher sucks ass...

How do i learn limits? What are they for? This really look like useless rocket science now, my teacher sucks ass, didnt even told us for what is this crap for, we are just doing random crap now

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You need them for derivation and integration

And what the hell are these things and what are they for?

try disney.com
come back here in a few years when you're old enough

I am 20

and you've never heard of derivation and integration?
perhaps suicide is the answer

I just got into university math now

Limits are important for estimating the value of a function where the function is technically undefined. Consider the function y=1/(x-1). In this function x=1 is undefined because you can't divide by 0. But you can calculate the y value at .9, .99, .999, and .9999. Then you can also calculate at 1.0001, 1.001, 1.01, and 1.1. This method allows you to see what value y is approaching as you get closer to the undefined value. As for why you need to know this: there is no day-to-day application besides practicing basic logic. Like any math above the basic algebra/geometry level, it only becomes important if you plan on going into a science/applied science.

not knowing antiderivation is one, and listing as two is plain wrong.

It's just an academia circlejerk. You'd only use it in some sort of specialized science field.

Let me see If i can get this: the limit is that value we cant get directly - because dividing by 0 is impossible - but we can estimate, by taking the numbers "around" it. I am from the pharmacy graduation course, looking for rational drug design and molecular modeling, will need a PhD to work on these things, and also a lot of math knowledge

>Implying rocket science is useless.

Its like, it looks like rocket science, but with no use, thats what i meant

Pretty much this. One example is literally rocket science, targeting systems can use integration (hundreds of calcs per second) to determine the position of a rocket in relation to its target.

math.stackexchange.com/

>newfags

Don't you want to know how equations act once you approach zero or approach infinity, for example? If you know the limit then you can do mental calculations and estimations because you know how the trend will continue because the limit is being approached. Useful in many fields of mathematics such as Calculus which has been brought up. Differential and Integral Calculus are based on the idea of limits and the change in X approaching zero. Check out the limit definition of the derivative, once you learn derivatives you can find the slope of any point on a graph and do tons of applications.

>Don't you want to know how equations act once you approach zero or approach infinity?
No.

Where i work, we have a series of cameras to inspect castings for imperfections. The camera is programed to read an area based off a line in the part, where the casting is anodized. It detects white vs black pixels in the image of the pictures, but where it is "gray" the program uses limits to detect where that line between white and black is. if you plan on getting into any form of programming, or engineering, you will need to understand limits. they are used in almost every automated production line.

Yeh that's fair enough.

In astrophysics we use it to do things like calculate luminosity of stars, or to calculate the electric field inside some insulating metal. We add up infinitesimally small layers from one edge of the metal to the other. Those would be the limits.

Or you can calculate the mass of a sphere by multiplying the density of the sphere at a certain radius, by the area at that radius. In that situation you would need to integrate from 0 to the Radius of the sphere.

This could be useful if you knew that the density of the metal changed the further out you went, and so you couldn't just do density * volume.

And yeh we can prove that sometimes when we allow a function to go to infinity, it will just reach a finite number. And so determining these limits can help us solve unintuitive questions.

>Implying people like learning and aren't overtly hostile toward facts.

A function is, in some cases, a description of physical process, what's called a model of how something behaves.

The limit, in that case, is the amount of work required to achieve the function's end result.

Does that help?

If you have a function that describes how Earth gets energy from the Sun, you can see what the Sun's total energy is in the limit. Limit is how far we think it can go.

And they never tell you what it's for. They don't actually want you to know how much you pay for your mortgage, and what your chances of doing that successfully are. Nope.

They will probably soon stop teaching simple maths altogether. Easier to govern.

You should learn English too.

>Implying that OP is speaking anything other than English.

I never implied that. I know it's a sad world we live in and that people are lazy as fuck. They think homework has no use because they aren't smart or have enough will to actually try and apply it outside of school. And I am well aware of the hostility towards factssociople want you to cuddle them and be socialable. They don't want you to correct them or learn new things with them. Only myself and my autistic friends want to learn and work hard outside of school, for everyone else the social media world is all that exists and all that is necessary.

Try and stay that way once you leave high school. Also, try and lose the "I'm smarter than people because I want to work hard and learn and other people don't." Being humble is a skill that we should all work on. You will always be a small fish, there's always a bigger pond.

Right? Shit insinuation is shit insult.

Learning the concept is REALLY easy, I swear. Using them for practical things CAN be really hard.

Seriously, to grasp the concept, all you've got to do is imagine some pattern like this:

1 + 1/2 + 1/4 + 1/8 ...

Where you just KEEP ADDING half of the last term forever. You an see how it will never get too big. And limits are a way to describe how big it could ever get.

What they are for is a much easier question. Once you know how they work, it really becomes a task to find something that they cannot be applied to. Predicting the rate at which liquid will drain from a container by it's own weight is one example. (e.g. A bathtub or something analogous)

I love that limit.

A guy walks into a bar and orders a beer, a colleague of his walks in and decides just to have half a point, the next guy walks in and does the same. More and more people walk in and just want half of what the previous guys ordered. Eventually the bartender just got sick of it and poured them 2 beers.

*Half a pint

It depends on how much was in the first beer, really.

Thx. I heard about this stuff of mental calculations and estimations
Interesting, i look for programming
Once i was trying to find the volume of a solid in highschool and the monitor said i was almost using calculus, guess it was what you said with the sphere
Yeah, i think i will change to a better university, make my grades better and switch, for the one i am aiming they try to make geniouses there, teaching the origins and complicating with time
I remember in school that this bathtub calculation have a formula. Was this formula found out by calculus o.O?

>Implying you're not full of shit. Good luck in life, thinking everyone has equal intelligence and works equally hard.

> o.O

It can be done manually (which takes... forever), or with calculus (which, if done manually, takes... forever).

> Implying he even implied that everyone has equal intelligence and works equally hard.

Jesus, man, try harder.

Engineering major here. Google that shit man, just sit down and study, you'll get it. There's enough good info online.

I was just implying that everyone is smarter than you. Perhaps it went over your head.

>mfw I actually learn something interesting on Sup Forums

Keep on trying to teach people, Sup Forumsros, it's actually really cool of you guys.

This. Also: look up a few videos on limits on YouTube. Tons of people with tons of different approaches to teaching it. Find someone you like that teaches it accessibly and you'll never regret it.

I enjoy teaching people. I have that passion for education and science, so being able to explain something and pass that knowledge on is cool. I think we should all try to do that when we can.

lol limits are easy. all you need to know is:
>sequence a_n is convergent to 0 if sum of all its elements (S_n = a_1 + a_2 + ... + a_n + ...) is convergent. You check this with convergence tests
>a_n is convergent to a (real number) if |a_n-a| is convergent to 0
for functions it's pretty much the same, just you need to expand it to its Taylor series

This. Mainly things in maths like discrete math are very case specific. If you understand this shit, know that when you work something out, you have a hack for it.

So for instance, suppose an algorithm didn't exist and you were the computer scientist in charge of routing algorithms in a network. How would the node (we need to update addresses in the transport layer). Now, if you were a typical retard, you wouldn't get shit done and the world wouldn't be any better. You would have some shitty algorithm that is sluggish as fuck cause it checks every fucking possible path. Now, if you applied yourself and understood graph theory, you might come up with something like Dijkstra's algorithm. You'll get promoted, and a blowjob, and the world is better for it. The former you would not contribute to society, and someone else would beat you to it. Your job security and social life would be minimal. But remember, that is one case scenario out of countless ones that can be improved on. All this random shit we learn may be useless, or useful.

I look at it like when they grabbed rope in the boondock saints. Had they not had the rope, the scene may have been boring and the movie would have ended sooner and they'd've died.

Pick a function, any function. 1/x, sin(x), doesn't matter. Pick any x-value, and tell me what's going on around that x-value. Take values closer and closer to it without actually plugging it in, what number do they start tending to?

For example, try f(x) = (x^2-2x)/(x-2).
What happens when you plug in 2? Your calculator yells at you.
So try plugging in 1.9, that should be fine. Then try 1.99, 1.999, 1.9999 and so on.
Try it from the other side, 2.1, 2.01, 2.001, 2.0001 and so on. What results do those answers give you?
You may not know what this function looks like (hint: it's y=x but I cut out it's ability to plug in x=1) but you can tell from those numbers that right before this random hole in the function, from either side, it looks like it's tending towards f(2) = 2.

And that's what limits are, a way to analyze a function as the independent variable approaches a certain value. For most functions and most values, you can probably just plug it in and call it a day. But if something werid's going on there, you want to probe around and see what's up.

This comes in handy for derivatives (finding slope for functions that aren't straight lines) and integrals (finding area of shapes that aren't rectangles, triangles, etc.). It seems useless now, and truth be told, most of the limits you'll be doing when you do derivatives/integrals are really trivial (you'll probably see infinity or 0 for the answer a million times), but understanding that you can look at a problem and see what happens when you make things infinity big or infinitely small is a big deal.

>but I cut out it's ability to plug in x=1
I meant x=2, fack

>Being at the level when you understand a concept and think it's cool to make it more complicated when people ask you for help.

If someone doesn't understand limits, why even bring up taylor series? And why use full mathematic notation to describe it rather than explain conceptually.

Also, OP never asked about convergence rules.

This is why people dislike intelligence, because this is the sort of response that they get when asking for help.

It's just a fancy way of saying "This thing is equal to something else but not really cuz you aren't allowed to do that," for example, you can't divide 1 by 0, but you could take the limit of 1/x as x approaches 0, of course, it depends on which side you approach 0 from too.

It's like if you're gay but live in a really oppressive religious community that doesn't let you be gay so you fuck traps instead so it's not gay but really it is gay in principle. Or something.

It's mostly a mindfuck thing.

That's the good news though. It's better if you *grok* it, but even if you don't, you can still use them effectively.

The main thing to keep in mind is that calculus is *continuous* mathematics. That is, smooth things that be whacked up into an infinite number of pieces.

It's probably the infinity bit that's fucking with you.

Nothing "goes to infinity" or any of that bullshit, what you're doing is analyzing things that you could, in theory, chop up forever.

Think of the old joke:

A genie shows up to a mathematician and an engineer and shows them a super hot woman. The genie says, OK, she'll let you bend her over the desk she's sitting on, but you can only go half the distance to the desk. Then half more, half more, etc etc etc.

The mathemician sighs: "I can never get there."

The engineer takes off his pants: "I can get closer enough."

OK, back to the explanation: When you get told about delta x over delta y and they run it out a couple times to show you what's happening (assuming you're starting with the usual example of the slope of a tangent line), that's the "engineer" view.

The "mathematician" view is, as it turns out, you can use some definitions and symbolic manipulation to actually get to the value that the "engineer" view is getting closer and closer too.

That's your limit.

It's an actual thing, you just have to do some wacky work to find it.

Of coures, the thing to keep in mind is that not all functions *have* limits.

Sometimes you just can't get there from here (like there's a big trap door in front of the desk in the joke).

All a limit is is a value that your function approaches (you'll also hear "converges upon").

Just think: "Yo bra, if you keep driving this direction we're gonna end up in da ocean."

No, it's like "I'm not touching you, why are you getting mad, I'm not even touching you". When your hand is like 2 nanometers above them.

It's not intelligence. Did these people fail technical writing classes? You need to know your audience. You also need to develop fundamental ideas about how to educate people and use them.

Unfortunately, these people slip through the cracks, especially when it comes to math. They get a good teacher that explains things to them in such a way a bag of rocks can understand, then they grow up to write school textbooks without understanding the subject matter well enough to state it simply, let alone accurately using educational fundamentals.

And because of one moron doing a disservice to thousands, you have thousands of morons capable of dis-servicing more. It's a snowball effect.

And in my opinion, functions are explained completely wrong, always and for some reason people that think they understand them, don't.

I believe that it starts in high school, there are too many kids per teacher, and so they just try and get through the syllabus and if kids don't follow along, it's their fault.

Unless you have a passion for learning, which most kids don't at that age, it will be hard to keep up. And so lot's of kids end up giving up and thinking that it's too hard for them.

Essentially it's the teachers that are failing them unfortunately.

Also, who do you think is writing textbooks? It's not just college dropouts.

I agree with you on the snowball effect. The importance of science and maths needs to be stressed from the beginning.

It's uselessness is conditional. Unless you're developing something or are an astronaut, i challenge you to find a way to use its principles in trade. Schools should prioritize feasible mathematics and leave the abstract shit for hard science majors.

My mind is blown, i asked for help and i got it. I love you guise (you) (you)

Process control, in a nutshell.

take a_n = 2^n/n! as an example
sum from n=1 to infinity 2^n/n! is convergent by d'Alembert's criterion (lim_(n->inf) |a_(n+1)/a_n| = lim_(n->inf) |2*2^n*n!/(2^n*(n+1)*n!)| = lim_(n->inf) |2/(n+1)| = 0 < 1)
indeed, sum from n=1 to infinity 2^n/n! = 2+4/2+8/6+16/24+...=e^2 (where e is Euler's constant). Thus, by necessity a_n = 2^n/n! converges to 0 in infinity.

Oh I agree that high level maths should be optional. But I am still pushing for maths, and one of the sciences along with english to be mandatory until graduation of high school.

The story of "I just want to be a tradie" is a cop out. You can be a tradie for sure, but it should be a choice rather than, "I have nothing else that I can do because I didn't give a fuck in school and just dropped out". You should need to complete Year 12 (Australian here) Maths and Science to be able to leave high school. But as you said, advanced calculus and theoretical physics doesn't need to be included in it.

Just send me the Latex file.

You are hired to be the calculus teacher. She just says a lot of crap and dont put it out like you did

You can't run a successful restaurant or factory without an understanding of quadratic equations and systems of equations. You will go bankrupt.

take $a_n = \frac{2^n}{n!}$ as an example
$\sum_{n=1}^\infty \frac{2^n}{n!}$ is convergent by d'Alembert's criterion
\[\lim_{n\to\infty} |\frac{a_{n+1}}{a_n}| = \lim_{n\to\infty} |\frac{2\cdot 2^n n!}{2^n (n+1) n!}| = \lim_{n\to\infty} |\frac{2}{n+1}| = 0 < 1\]
indeed, $\sum_{n=1}^\infty \frac{2^n}{n!} = 2+\frac{4}{2}+\frac{8}{6}+\frac{16}{24}+\ldots = e^2$ (where $e$ is Euler's constant). Thus, by necessity $a_n = \frac{2^n}{n!}$ converges to $0$ in infinity.

Use \Big| if you're using fractions (See the left limit) for nicer formatting.

Cheers for actually including the file, I was in the middle of writing it up myself.

I use \left| and right| usually in this case. Didn't compile that so didn't notice the problem.

Differentiation. Derivation is when you create or derive somelike like a formula

That's probably nicer for the delimiters. I'm used to using the \Big for adding definite limits when evaluating integrals, as I only need one.

What field are you in? Or are you still at Uni? Writing from memory without compiling took me a while, I remember first starting I has to compile every sentence haha.

Math is not even useful for any real world application of any use until you learn limits,calculus, and differential equations

CS, first year.

Bullshit. Arithmetic and algebra are vital to everyday life

Ah that probably explains it. I'm in Astrophysics, 2nd year. Latex still isn't pushed and most people in my year still don't use it unfortunately. But I got my first paper published this year and it was very useful knowing how to properly typeset.

Agreed

Wut. How do you count how much money you have? That's maths man.

Nobody teaches us Latex in CS. All we had so far was C, bash, x86 assembly and Java.

Really user? I am an engineering major and we hardly use calc or differential equations. Most of the problems we solve are solved with algebraic equations.

Forgot SML and Verilog/VHDL but nobody remembers them for real.

Consider yourself lucky. The languages we were introduced to were Matlab, R, Fortran. Like seriously... I'd much prefer learning Python.

What Uni are you studying at?

That's cause engineering is just for physicists who don't understand physics haha. And then when engineers don't understand maths, you get Architects.

agh.edu.pl/

>learning Python
Sure, why not? If only a semester took 2 weeks.

That's not how you meme arrow dummy

Suicide is only the answer for people who think they know math and call it derivation when it's "differentiation".

It's used frequently when running scripts with our x-ray and radio telescopes, but because of course work I never get a chance to practice it.

I'm
curtin.edu.au/

What if you're deriving the rate of change of a function?

what's it for? functional optimization and basically all of introductory calculus.

the derivative of a function is a new function describing the slope of the original function at any given element in the original's domain.

the integral of a function undoes its derivation, and gives you the area underneath the integrated curve.

the most basic example of the usefulness of derivation/integration is in physics. position (displacement) is the original function, velocity is its derivative, and acceleration is the derivative of velocity. if you know just one of these functions, then you can use calculus to find out all of the others.

limits are useful in understanding the behavior of a curve at a point where it is technically undefined. think about when you look at your speedometer while you're driving. you only look once in a while. but limits kind of fill in the information in between the times that you actually observe. this is an oversimplified version of the explanation but it's all i can think of right now.

But for actual everyday usefulness when are you ever just given a function describing displacement, velocity, or acceleration?

>waste of life tier
Good that i am on pharmacy

if not CS, I would probably pick up linguistics or art. So I guess I'm doomed

you aren't. but the more data points you observe, the closer you come to having a smooth curve and the more closely you can approximate a function to the real situation.

>computer science
Rip me.

allow me to explain one more reason why EVERY SINGLE PERSON should be required to know calculus:

the development of calculus was one of the most significant achievements over the course of human history, and the thought processes required to understand it will make you a better critical thinker in general and, by virtue of that, a better person in general. people need the general critical thinking skills that calculus requires in order to not wind up pumping gas and flipping bugers. you want to be good at THINKING? learn calculus.

>critical thinking skills this critical thinking skills that
except calculus is little about thinking and more about shitton of theory
If you want to develop critical thinking, discrete mathematics is all you need.

understanding the theory requires you to think. it requires you to challenge your own notion of what constitutes "proof" and what is not proof.

>little about thinking and a shitton of theory

do you live in a world where you just memorize theory without understanding the reasoning behind it? enjoy CS

Well you should have learned them years ago, but I guess you didnt. Depending on what you are looking for in a degree, you may or may not ever use them.

However, it's a very good concept to know from a logic standpoint (which you can apply to anything).

A limit is applied to a function, just like addition or subtraction. So let's take a function

F (x) = 3 x + 5.

Now let's "take a limit" as x approaches infinity. So imagine what happens to F (x) as x gets closer to infinity. 3 times infinity is infinity, ading five also is infinity. So the limit as x approaches infinity is infinity.

This example is very basic.

Now for a more complicated example.

Let's say you have this function:

F (x) = (x^2 + x)/(e^x)

And let's take the limit as x approaches infinity again. You will get infinity squared plus infinity, divided by e to the infinity.

If you think about it, e to the infinity is a much larger value than the top half of the expression, therefore you can see it as (1/100000000000) which is pretty close to zero.

As you've probably guessed, this means the limit of the function as x approaches infinity is 0. There is a lot of math inbombed in proving this, but this is the concept.

In terms of application, limits mostly apply to rates, or how things change over a parameter like time or voltage.

It also applies to scale ups.

If you were doing a small scale reaction od x and y, with .03444 cal heat produced per mole, you can quickly check if you reaction is feasible, by taking the limit.

F (x) = .0344cal × Xmol.

Limit as x approaches infinity will give you infinity.

This is a very bad example, and it's more important in flow rates and pressure, but you can see how they help you figure things out quickly.

Your teacher may be fine, because limits are mostly a tool to teach derivatives. Which relate physical properties in a succinct manner. He/she may teach those much better.

god i love this thread